I develop a new analysis of English “weak necessity” modals 'should'
and 'supposed
to' that is motivated by novel observations of extra-weak meanings in some
environments. For example, *'supposed to'* in (1a) gives rise to a meaning
that can be paraphrased as the weaker modal statement in (1b).
(1) A: Can you please pick up a book for me at the office?
1.
B: I don’t know... Are we supposed to be back on campus without a Covid
test?
2.
B′: I don’t know... Is it okay for us to be back on campus without a
Covid test?
I argue that this evidence of weak readings suggests that these modal verbs
exhibit a type of variable force. Sentences with weak necessity modals
express universal force in positive sentences and existential force under
negation. The analysis will build on an analogy with free-choice
disjunction that assumes a basic weak meaning that strengthens in
upward-entailing environments (Fox, 2007; Bassi and Bar-Lev, 2016). These
modals' "neg-raising" property then follows as an immediate consequence.
I further propose that the precise distribution of the strengthened
readings is governed by the polarity-sensitive nature of the modals (cf.
Iatridou and Zeijlstra, 2013; Homer, 2015). In particular, I argue that the
polarity sensitivity of the modals is the result of the association of
their domains with a covert 'even' (cf. Lahiri, 1995; Crnicˇ, 2014, 2019
for NPI 'any'). I then show how rhetorical effects observed in questions
like (1a) can be generated with independently-motivated mechanisms proposed
in Iatridou and Tatevosov (2016) to explain the effects of 'even' in
questions.